5.3.03-00 Hall effect in metals Physical structure of matter - niser

Physical structure of matter Solid-state Physics
5.3.03-00 Hall effect in metals
What you need:
Hall effect, Cu, carrier board 11803.00 1
Hall effect, zinc, carrier board 11804.01 1
Coil, 300 turns 06513.01 2
Iron core, U-shaped, laminated 06501.00 1
Pole pieces, plane, 30�30�48 mm, 2 06489.00 1
Power supply 0-30 VDC/20 A, stabil 13536.93 1
Power supply, universal 13500.93 1
Universal measuring amplifier 13626.93 1
Teslameter, digital 13610.93 1
Hall probe, tangent., prot. cap 13610.02 1
Digital multimeter 07134.00 1
Meter, 10/30 mV, 200°C 07019.00 1
Universal clamp with join 37716.00 1
Tripod base -PASS- 02002.55 1
Support rod -PASS-, square, l = 250 mm 02025.55 1
Right angle clamp -PASS- 02040.55 2
Connecting cord, l = 750 mm, red 07362.01 6
Connecting cord, l = 750 mm, blue 07362.04 5
Connecting cord, l = 750 mm, black 07362.05 2
Complete Equipment Set, Manual on CD-ROM included
Hall effect in metals P2530300
What you can learn about …
� Normal Hall effect
� Anomalous Hall effect
� Charge carriers
� Hall mobility
� Electrons
� Defect electrons
Principle:
The Hall effect in thin zinc and copper
foils is studied and the Hall coefficient
determined. The effect of
temperature on the Hall voltage is
investigated.
Hall voltage as a function of magnetic induction B, using a copper sample.
Tasks:
1. The Hall voltage is measured in
thin copper and zinc foils.
2. The Hall coefficient is determined
from measurements of the current
and the magnetic induction.
3. The temperature dependence of
the Hall voltage is investigated on
the copper sample.
234 Laboratory Experiments Physics
PHYWE Systeme GmbH & Co. KG · D-37070 Göttingen

Related topics
Normal Hall effect, anomalous Hall effect, charge carriers, Hall
mobility, electrons, defect electrons.
Principle
The Hall effect in thin zinc and copper foils is studied and the
Hall coefficient determined. The effect of temperature on the
Hall voltage is investigated.
Equipment
Hall effect, Cu, carrier board 11803.00 1
Hall effect, zinc, carrier board 11804.01 1
Coil, 300 turns 06513.01 2
Iron core, U-shaped, laminated 06501.00 1
Pole pieces, plane, 30�30�48 mm, 2 06489.00 1
Power supply 0-30 VDC/20 A, stabil 13536.93 1
Power supply, universal 13500.93 1
Universal measuring amplifier 13626.93 1
Teslameter, digital 13610.93 1
Hall probe, tangent., prot. cap 13610.02 1
Digital multimeter 07134.00 1
Meter, 10/30 mV, 200 °C 07019.00 1
Universal clamp with join 37716.00 1
Tripod base -PASS- 02002.55 1
Support rod -PASS-, square, l = 250 mm 02025.55 1
Right angle clamp -PASS- 02040.55 2
Fig. 1: Experimental set-up for the Hall effect in metals.
Hall effect in metals
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5.3.03
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Connecting cord, l = 750 mm, red 07362.01 6
Connecting cord, l = 750 mm, blue 07362.04 5
Connecting cord, l = 750 mm, black 07362.05 2
Tasks
1. The Hall voltage is measured in thin copper and zinc foils.
2. The Hall coefficient is determined from measurements of
the current and the magnetic induction.
3. The temperature dependence of the Hall voltage is investigated
on the copper sample.
Set-up and procedure
The layout follows Fig. 1 and the wiring diagram in Fig. 2.
– Arrange the field of measurement on the plate midway
between the pole pieces.
– Carefully place Hall probe in the centre of the magnetic field.
– The measuring amplifier takes about 15 min. to settle down
free from drift and should therefore be switched on correspondingly
earlier.
– To keep interfering fields at a minimal level, make the connecting
cords to the amplifier input as short as possible.
– Take the transverse current I for the Hall probe from the powersupply
unit 13536.93. It can be up to 15 A for short periods.
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Fig. 2 Circuit diagram for the Hall effect.
The Hall probe will show a voltage at the Hall contacts even in
the absence of a magnetic field, because these contacts are
never exactly one above the other but only within manufacturing
tolerances. Before measurements are made, this voltage
must be compensated with the aid of the potentiometer as follows:
– Disconnect the transverse current I.
– Set the measuring amplifier to an output voltage of 1 V, for
example, by adjusting the compensation-voltage.
(h e = 10 4 Ω, amplification = 10 5 )
– Connect the transverse current.
– Twist the connecting cords between hall voltage sockets
and amplifier input in order to avoid as much as possible
stray voltages.
– Adjust the compensating potentiometer, using a screwdriver,
until the instrument again shows an output voltage of
1V.
– Repeat this operation several times to obtain a precise
adjustment.
The determination of the Hall voltage is not quite simple since
voltages in the microvolt range are concerned where the Hall
voltages are superposed by parasitic voltages such as thermal
voltages, induction voltages due to stray fields, etc. The following
procedure is recommended:
– Set the transverse current � to the desired value.
– Set the field strength B to the desired value (on the power
supply, universal, 13500.93).
– Set the output voltage of the measuring amplifier to about
1.5 V by adjusting the compensation-voltage.
– Using the mains switch on the power supply unit, switch the
magnetic field on and off and read the Hall voltages at each
on and off position of the switch (after the measuring amplifier
and the multi-range meter have recovered from their
Hall effect in metals
peak values). The difference between the two values of the
voltage, divided by the gain factor 10 5 , is the Hall voltage U H
to be determined.
Theory and evaluation
If a current I flows through a strip conductor of thickness d
and if the conductor is placed at right angles to a magnetic
field B, the Lorentz force
F �
= Q (n � x B �
)
acts on the charge carriers in the conductor, n being the drift
velocity of the charge carriers and Q the value of their charge.
This leads to the charge carriers concentrating in the upper or
lower regions of the conductor, according to their polarity, so
that a voltage – the so-called Hall voltage U H – is eventually
set up between two points located one above the other in the
strip:
U H � R H · B · I
d
R H is the Hall coefficient.
The type of charge carrier can be deduced from the sign of the
Hall coefficient: a negative sign implies carriers with a negative
charge (“normal Hall effect”), and a positive sign, carriers with
a positive charge (“anomalous Hall effect”). In metals, both
negative carriers, in the form of electrons, and positive carriers,
in the form of defect electrons, can exist. The deciding
factor for the occurrence of a Hall voltage is the difference in
mobility of the charge carriers: a Hall voltage can arise only if
the positive and negative charge carriers have different mobilities.
The measurements for copper shown in Fig. 3 are related by
the expression UH � B. Linear regression using the relation
UH = a + bB shows these values to be represented by a
straight line with the slope b = -0.0384 · 10 -6m2 /s and a standard
deviation sb = 0.0004 · 106m/s. From this, with
d =18·10 -6 m and I = 10 A, we derive the Hall coefficient
RH = –(0.576 ± 0.006) · 10-10 m3 /As.
25303-00 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
.

Fig. 3: Hall voltage as a function of magnetic induction B,
using a copper sample.
The measurements shown in Fig. 4 confirm for copper the
relation UH � I Linear regression with the relation UH a + bI
yields a straight line with slope b = – 0.770 · 10 -6 V/A and
standard deviation sb = 0.005 · 10-6 V/A. From this, with
d =18· 10 -6 m and B = 0.25 T, we derive the Hall coefficient
RH = – (0.554 ± 0.004) · 10-10 m3 /As.
Fig. 4: Hall voltage as a function of current I, using a copper
sample.
Hall effect in metals
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Fig. 5: Hall voltage as a function of magnetic induction B,
using a zinc sample.
The zinc sample shows an anomalous Hall effect, in that the
Hall voltage has a positive sign. The measurements shown in
Fig. 5 confirm for zinc the relationship UH � B. Linear regression
using the expression UH = a + bB gives a straight line with slope
b = 20.7·10 -6 m2 /s and standard deviation sb = 0.4·10-6 m/s.
From this, with d = 25·10 -6 m and I = 12 A, we obtain the Hall
coefficient
RH = (4.31 ± 0.01) · 10-11 m3 /As.
Fig. 6: Hall voltage as a function of current I, using a zinc
sample.
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The measurements shown in Fig. 6 confirm for zinc the relation
UH � I. Linear regression using the expression UH =
a + bI gives a straight line with siope b = 0.40·10 6 V/A and
standard deviation sb = 0.01·10 -6 V/A. From this, with
d =25·10 -6 m and B = 0.25 T, we obtain the Hall coefficient
RH = (4.00 ± 0.01)·10 -11 m 3 /As.
If the sample temperature is varied, we find, disregarding disturbing
thermal voltages, that the Hall voltage in metals is not
temperature dependent.
4
Hall effect in metals
If the measured values of the Hall coefficients are compared
with those given in the literature
(copper: R H = – 0.53·10 -10 m 3 /As; zinc: R H = 10·10 -11 m 3 /As),
it is noteworthy that the values for zinc show a distinct difference.
This, it may be presumed, is attributable to disturbing
secondary effects particularly at the contact points. Among
these we may mention the Ettinghausen effect, the Peltier
effect, the Seebeck effect, the first Righi-Leduc effect and the
first Ettinghausen-Nernst effect. lt is possibly due also to
impurities in the test material (99.95% purity).
25303-00 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen